4) Consider the following mass spring damper system: k m2 u(t) Assuming that y, > y1, equation of motion (EOM) for this system can be obtained by applying the Newton's second law: F, = mỹ (i. e. RHS is positive) Then, equations are written as: m,ỹi = k2(V2 – Y1) – k,yı – cy, (1) m2y2 = u(t) - k2(y2 – Yı) (2) where u(t) is the input function to the system. Take m, = 1 kg, m2 = 2 kg, c = 10 Ns/m and ki = 10 N/m, k2 = 20 N/m. Then, answer the following questions. a) Find the transfer functions G,(s) = 1O and G2(s) = 4O U(s) U(s) b) Use Laplace transform method and obtain the displacements in Laplace space (i.e. s domain) Y,(s) and Y2(s) utilizing initial conditions y, (0) = 0, y2(0) = 1, ÿ; (0) = 1 and y2(0) = 0. Use Cramer's rule for the solutions of Y,(s) and Y2(s). c) Using Inverse Laplace transformation, obtain displacements in time space (i.e. time domain) Y1(t) and y2(t) if,

4) Consider the following mass spring damper system: k m2 u(t) Assuming that y, > y1, equation of motion (EOM) for this system can be obtained by applying the Newton's second law: F, = mỹ (i. e. RHS is positive) Then, equations are written as: m,ỹi = k2(V2 – Y1) – k,yı – cy, (1) m2y2 = u(t) - k2(y2 – Yı) (2) where u(t) is the input function to the system. Take m, = 1 kg, m2 = 2 kg, c = 10 Ns/m and ki = 10 N/m, k2 = 20 N/m. Then, answer the following questions. a) Find the transfer functions G,(s) = 1O and G2(s) = 4O U(s) U(s) b) Use Laplace transform method and obtain the displacements in Laplace space (i.e. s domain) Y,(s) and Y2(s) utilizing initial conditions y, (0) = 0, y2(0) = 1, ÿ; (0) = 1 and y2(0) = 0. Use Cramer's rule for the solutions of Y,(s) and Y2(s). c) Using Inverse Laplace transformation, obtain displacements in time space (i.e. time domain) Y1(t) and y2(t) if,

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

See similar textbooks

Similar questions

The equation of motion of a certain mass-spring-damper system is 5x'' + cx' +10x = f(t). Suppose that f(t) = Fsin(wt). Define the magnitude ratio as M = X/F. Determine the natural frequency w_n, the peak frequency w_p, and the peak magnitude ratio M_p for damping ratio = 0.1 and the damping ratio = 0.3
design a simple mass-spring-damper, indicate the values of the system, and provide an equation where the system is in a resonant state.
Find the period and make a graph of "xv/s t", of a mass-spring system with elastic constant K=8 Kg/s² and m=2 Kg, which moves from its equilibrium position ma, distance d = 0.5m . Make a graph of damped and undamped.
Figure 1 shows a system comprising a bar with mass m-12 kg and the length of the bar L=2 m, two springs with stiffness kt=1000 N-m/rad and k = 2000 N/m, one damper with damping coefficient c=50 N-s/m and two additive masses at the end of the bar, where each mass (M) is equal to 50 kg. The rotation about the hinge A, measured with respect to the static equilibrium position of the system is 0 (t). The system is excited by force (F) so find the state space representation of the system if the output y=ġ(t).
Question 1 Define how resonance occurs in a dynamic system? What must you take into account from preventing this from occurring? Finally, design a simple mass-spring-damper, indicate the values of the system, and provide an equation where the system is in a resonant state.
Question1B Finally, design a simple mass-spring-damper, indicate the values of the system, and provide an equation where the system is in a resonant state.
A spring-mass-damper system oscillating about the horizontal surface is subjected to anexternal force of F = 300 sin (6)(t), where 300 is in Newtons and 6 is in radians per second. Thesystem has a mass 90 [kg], a damping coefficient of 78 [N ⋅ s/m] and a spring constant of300 [N⁄m]. The system is both given an initial displacement of 1.2 [m] and an initial velocity of 1.4[m⁄s].a. Using Method of Undetermined Coefficients, determine the particular solution for thedisplacement function.b. Determine the unknown coefficients for the homogeneous solution using the initialconditions (Note: the external force already works at t = 0).c. Determine the position, velocity, and acceleration of the system after 10 seconds.
Q3.Consider a spring–mass–damper system with m = 80 kg, c = 15 kg/s, and k = 1500 N/m with an impulse force applied to it of 1200 N for 0.01 s. (C) Calculate the damped natural frequency of the system (D) Calculate the system response to the impulsive force at time t = 1 s
Between a solid mass of 10 kg and floor, two slab of isolator, natural rubber and feltare kept in series as shown in Figure Q1(b). The natural rubber slab has a stiffnessof 3000 N/m and an equivalent viscous damping coefficient of 110 Ns/m. The feltslab has a stiffness of 12,200 N/m and an equivalent viscous damping coefficient of170 Ns/m. (i) Sketch the single degree of freedom spring-mass-damper system(ii) Determine the undamped and damped natural frequencies of the system inthe vertical direction. Neglect the mass of the isolator
A spring-mass-damper system has mass of 80 kg, stiffness of 2500 N/m, and damping coefficient of 250 kg/s Calculate the undamped natural frequency, the damping ratio, and the damped natural frequency Does the solution osciliate?
A block-spring system has a maximum restoring force Fmax = 0.1 N. If the amplitude of the motion is A = 0.01 m and the mass of the block is m = 100 g then the angular frequency w is equal to
Considering that the displacement motion (x) of the single degree of freedom mass-spring-damper system given in the figure is measured from the static equilibrium position, draw the: a) free body diagram of the system. b) Derive the equation of motion. c) Find its natural frequency. d) When x (0) = 0.01 m is pulled down at t-0 and when x (0) = 0 m / s is released, its movement x (t) is m = 3 kg, b-12 N / m / s and Find it using the values of k = 120 N / m. e) Find the transfer function of the system when there is a force input of F = 10 N downward (in the + x direction) to the object. f) Show this transfer function with a block diagram.